{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "427a089b-9140-41fb-b5e6-3cf39f0d6ca8",
      "metadata": {},
      "source": [
        "# Analysis and simulation of a rectangular waveguide"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "16b1aa80-81cd-477c-b603-35187b994e18",
      "metadata": {},
      "source": [
        "In this excercise a rectangular waveguide filled by a dielectric is designed and analysed, according to the following parameters:\n",
        "\n",
        "$$ a = 101 \\textit{mm} $$\n",
        "$$ b = 40.4 \\textit{mm} $$\n",
        "$$ \\epsilon_r = 3.8 $$\n",
        "\n",
        "The dielectric behaviour in the electromagnetic field is then described by the following constants:\n",
        "\n",
        "$$ \\mu = \\mu_0 $$\n",
        "$$ \\epsilon = \\epsilon_0 \\epsilon_r $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "427ccee4-3be3-4dd8-bed5-88f62368b5e4",
      "metadata": {
        "tags": [
          "remove_cell"
        ],
        "vscode": {
          "languageId": "octave"
        }
      },
      "outputs": [],
      "source": [
        "a = 0.1010;\n",
        "b = 0.0404;\n",
        "e_r = 3.8;\n",
        "m = 1;\n",
        "n = 4;\n",
        "l = 1;\n",
        "\n",
        "mu_0 = 4e-7*pi;\n",
        "e_0 = 8.85e-12;\n",
        "c_0 = 1/sqrt(mu_0*e_0);\n",
        "mu = mu_0;\n",
        "e = e_0*e_r;\n",
        "c = 1/sqrt(mu*e);\n",
        "\n",
        "E0 = 1;\n",
        "\n",
        "f = 7.68e9;\n",
        "w = 2*pi*f;\n",
        "\n",
        "k = w*sqrt(mu*e);\n",
        "kc = sqrt((m*pi/a)^2 + (n*pi/b)^2);\n",
        "be = sqrt(k^2-kc^2);\n",
        "\n",
        "P = 50;  % Grid precision\n",
        "\n",
        "[X,Y] = meshgrid(linspace(0,a,P),linspace(0,b,P));"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7e0d3d16-da82-409b-8c5e-e9ab452daf90",
      "metadata": {},
      "source": [
        "## Properties of the transmitted mode"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "f3695b5c-bf2b-4592-8cb9-7385e37e059e",
      "metadata": {
        "tags": [
          "remove_cell"
        ],
        "vscode": {
          "languageId": "octave"
        }
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Fc14 = 7.6532e+09\n"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "% Cutoff frequency of the analysed mode\n",
        "Fc14 = c_0/2/sqrt(e_r)*sqrt((m/a)^2+(n/b)^2)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "40249f48-2b9e-4abd-bc92-840d135167ea",
      "metadata": {
        "tags": []
      },
      "source": [
        "The transmitted mode being analysed is the $\\textit{TM}_{(1,4)}$, with cutoff frequency\n",
        "\n",
        "$$ f_{c(m,n)} = \\frac{1}{2\\sqrt{\\mu\\epsilon}} \\sqrt{\\left(\\frac{m}{a}\\right)^2 + \\left(\\frac{n}{b}\\right)^2} \\approx 7.65 \\textit{GHz} $$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a72024a1-abab-4534-b1dd-01e6d872fb68",
      "metadata": {
        "tags": []
      },
      "source": [
        "### Field components\n",
        "\n",
        "The mode is _transverse magnetic_, which means that the longitudinal component of the magnetic field is null ($H_z = 0$).\n",
        "\n",
        "The longitudinal component of the electric field is:\n",
        "\n",
        "$$ E_z(x,y,z) = E_0 \\sin \\frac{m \\pi x}{a}\\sin\\frac{n \\pi y}{b} e^{-j\\beta z} $$\n",
        "\n",
        "where $\\beta$ is a function of the frequency of the transmitted wave and of the geometry of the waveguide ($a$ and $b$). \n",
        "\n",
        "For TM modes the Maxwell equations (written in phasor form for linear media and without sources) can be reduced as follows:\n",
        "\n",
        "$$ \\vec{E_t} = \\frac{-j \\beta}{k_c^2} \\nabla E_z $$\n",
        "$$ \\vec{H_t} = \\frac{\\hat{z} \\times \\vec{E_t}}{Z_{TM}} $$\n",
        "\n",
        "where $Z_{TM} = \\frac{\\beta}{\\omega\\epsilon}$ is the modal impedance.\n",
        "\n",
        "All the other components can then be calculated as a function of the longitudinal component of the electric field:\n",
        "\n",
        "$$ E_x = \\frac{-j \\beta}{k_c^2}\\frac{m\\pi}{a} E_0 \\cos \\frac{m \\pi x}{a}\\sin\\frac{n \\pi y}{b} e^{-j\\beta z} $$\n",
        "$$ E_y = \\frac{-j \\beta}{k_c^2}\\frac{n\\pi}{b} E_0 \\sin \\frac{m \\pi x}{a}\\cos\\frac{n \\pi y}{b} e^{-j\\beta z} $$\n",
        "$$ H_x = \\frac{ j \\omega \\epsilon}{k_c^2}\\frac{n\\pi}{b} E_0 \\sin \\frac{m \\pi x}{a}\\cos\\frac{n \\pi y}{b} e^{-j\\beta z} $$\n",
        "$$ H_y = \\frac{-j \\omega \\epsilon}{k_c^2}\\frac{m\\pi}{a} E_0 \\cos \\frac{m \\pi x}{a}\\sin\\frac{n \\pi y}{b} e^{-j\\beta z} $$\n",
        "\n",
        "#### Electric field representation "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "654bca41-cf11-4f0d-a15d-d13922ed3b27",
      "metadata": {
        "tags": [
          "remove_cell"
        ],
        "vscode": {
          "languageId": "octave"
        }
      },
      "outputs": [
        {
          "data": {
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"
          },
          "metadata": {
            "image/png": {
              "height": 900,
              "width": 1200
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "% Phase in the time dimension \n",
        "p = pi/4;    # Change it from 0 to 2*pi to see the variation of the E field\n",
        "% Phase in the z dimension\n",
        "z = 0;       # Change it from 0 to 2*pi to see the variation of the E field\n",
        "\n",
        "EX0 = -j*E0*be*m*pi/kc^2/a;\n",
        "EY0 = -j*E0*be*n*pi/kc^2/b;\n",
        "EZ0 = E0;\n",
        "\n",
        "% Phasorial fields\n",
        "Ex = EX0.*cos((m*pi/a).*X).*sin((n*pi/b).*Y);\n",
        "Ey = EY0.*sin((m*pi/a).*X).*cos((n*pi/b).*Y);\n",
        "Ez = EZ0.*sin((m*pi/a).*X).*sin((n*pi/b).*Y);\n",
        "\n",
        "% Vector fields\n",
        "Fx = real(Ex.*exp(i*p).*exp(j*be*z));\n",
        "Fy = real(Ey.*exp(i*p).*exp(j*be*z));\n",
        "Fz = real(Ez.*exp(i*p).*exp(j*be*z));\n",
        "\n",
        "F = sqrt(Fx.^2+Fy.^2+Fz.^2);\n",
        "\n",
        "EX0_ = abs(EX0);\n",
        "EY0_ = abs(EY0);\n",
        "EZ0_ = abs(EZ0);\n",
        "\n",
        "figure(\"position\", [0 0 1200 900])\n",
        "colormap(\"turbo\");\n",
        "subplot(2,2,1);\n",
        "imagesc([0 a],[0 b],Fx,[-EX0_,EX0_]);\n",
        "colorbar;\n",
        "title(\"X component\");\n",
        "subplot(2,2,2);\n",
        "imagesc([0 a],[0 b],Fy,[-EY0_,EY0_]);\n",
        "colorbar;\n",
        "title(\"Y component\");\n",
        "subplot(2,2,3);\n",
        "imagesc([0 a],[0 b],Fz,[-EZ0_,EZ0_]);\n",
        "colorbar;\n",
        "title(\"Z component\");\n",
        "subplot(2,2,4);\n",
        "imagesc([0 a],[0 b],F,[0,E0]);\n",
        "colorbar;\n",
        "title(\"ABS value\");"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "768afe71-880c-48c7-86d6-f31c94306ad8",
      "metadata": {},
      "source": [
        "### Frequency dependent properties\n",
        "\n",
        "Below are reported in a range of $[1.1 \\div 2]f_{c(1,4)}$ the main mode properties that are a function of frequency:\n",
        "\n",
        "* the propagation constant $\\beta = 2\\pi f \\sqrt{\\mu \\epsilon} \\sqrt{1-\\left(\\frac{f_{c(1,4)}}{f}\\right)^2}$\n",
        "\n",
        "* the group velocity $v_g = c \\sqrt{1-\\left(\\frac{f_{c(1,4)}}{f}\\right)^2}$\n",
        "\n",
        "* the phase velocity $v_f = \\frac{c}{\\sqrt{1-\\left(\\frac{f_{c(1,4)}}{f}\\right)^2}}$\n",
        "\n",
        "* the wavelength $\\lambda = \\frac{2 \\pi }{\\beta}$\n",
        "\n",
        "* the modal impedance $Z_{TM} = \\frac{\\beta}{2 \\pi f \\epsilon}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "31968a5e-6e20-4f8b-846f-29091da3d399",
      "metadata": {
        "tags": [
          "remove_cell"
        ],
        "vscode": {
          "languageId": "octave"
        }
      },
      "outputs": [],
      "source": [
        "F = linspace(1.1*Fc14, 2*Fc14);\n",
        "sqrt_f = sqrt(1-(Fc14./F).^2);\n",
        "\n",
        "be_f = (2*pi*sqrt(mu*e)).*F.*sqrt_f;\n",
        "vg_f = c.*sqrt_f;\n",
        "vf_f = c./sqrt_f;\n",
        "lm_f = (2*pi)./be_f;\n",
        "zm_f = be_f./(2*pi*e)./F;"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "c8974bb8-02cb-4fd4-b870-afb2100fd01d",
      "metadata": {
        "tags": [
          "remove_input"
        ],
        "vscode": {
          "languageId": "octave"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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"
          },
          "metadata": {
            "image/png": {
              "height": 900,
              "width": 1200
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "figure(\"position\", [0 0 1200 900])\n",
        "\n",
        "subplot(2,2,1);\n",
        "plot(F/1e9, be_f);\n",
        "title('Propagation constant \\beta [rad/m]');\n",
        "xlabel(\"Frequency [GHz]\");\n",
        "xlim([1.1*Fc14 2*Fc14]/1e9);\n",
        "grid on;\n",
        "\n",
        "subplot(2,2,2);\n",
        "plot(F/1e9, vg_f, F/1e9, vf_f);\n",
        "title('Group and phase velocities (v_g and v_f) [m/s]');\n",
        "xlabel(\"Frequency [GHz]\");\n",
        "legend('v_g', 'v_f');\n",
        "xlim([1.1*Fc14 2*Fc14]/1e9);\n",
        "grid on;\n",
        "\n",
        "subplot(2,2,3);\n",
        "plot(F/1e9, lm_f*1e3);\n",
        "title('Wavelength \\lambda [mm]');\n",
        "xlabel(\"Frequency [GHz]\");\n",
        "xlim([1.1*Fc14 2*Fc14]/1e9);\n",
        "grid on;\n",
        "\n",
        "subplot(2,2,4);\n",
        "plot(F/1e9, zm_f);\n",
        "title('Modal impedance Z_{TM} [\\Omega]');\n",
        "xlabel(\"Frequency [GHz]\");\n",
        "xlim([1.1*Fc14 2*Fc14]/1e9);\n",
        "grid on;"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Octave (xoctave)",
      "language": "Octave",
      "name": "xoctave"
    },
    "language_info": {
      "version": "7.3.0",
      "codemirror_mode": "octave",
      "file_extension": ".m",
      "mimetype": "text/x-octave",
      "name": "Octave",
      "nbconvert_exporter": "",
      "pygments_lexer": "octave"
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